Question

Question 7.1 - 7

A genetic experiment with peas resulted in one sample of offspring that consisted of 428 green peas and 161 yellow peas.

a. Construct a 90​% confidence interval to estimate of the percentage of yellow peas.

b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

Answer 1

Solution :

Given that,

n = 428 + 161 = 589

a) Point estimate = sample proportion = = x / n = 161 / 589 = 0.273

1 - = 1 - 0.273 = 0.727

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.273 * 0.727) / 589 )

= 0.030

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.273 - 0.030 < p < 0.273 + 0.030

(0.243 < p < 0.303)

b) No, the confidence interval include 0.25, so the true percentage could easily equal 25%